Stick Insect Climate PCA

Read in the packages. The working directory is wherever the R Notebook is located.

Read in the spreadsheet and take a look at the data. There is one outlier (acan-sp_68). I’m throwing it out here, but need to ask about original coordinates.

Map

Plot a leaflet map of the localities. The leaflet map is interactive. You can click on the localities and a flag with some metadata will pop up!

#use sourced plot_locs_leaflet script to plot localities
all_plot <- plot_locs_leaflet(loc)

Assuming "longitude" and "latitude" are longitude and latitude, respectively

all_plot

PCA-Genera

Climate Data

Obtain the bioclim layers for analysis. I’m using all 19 for this preliminary exploration. I plotted the first bioclim just to make sure nothing seems wonky.

##get worldclim data
w <- getData("worldclim", var = "bio", res = 0.5, lon = 173, lat = -35)

PCA by locality

This is a PCA of the climate data extracted for each locality, rather than a PCA of the total climate space.

Run the pca and check out variable loadings and proportion of variance explained by components.

#extract data from worldclim for each locality. Making this into a data frame with columns labeled so the row labeling lines up after I remove the NAs.
#extract data from worldclim for each locality.
coords <- data.frame(latitude = loc$longitude, longitude = loc$latitude)
loc.clim <- dplyr::bind_cols(loc, raster::extract(w, coords, method = "simple", df = TRUE)) %>% 
  na.omit() %>% 
  select(-ID)
#make a matrix of only bioclim values
clim.mat <- loc.clim[,grep("bio", names(loc.clim))] %>% as.matrix()
#run pca on climate variables
clim.pca <- prcomp(clim.mat, scale = TRUE)
summary.pca <- summary(clim.pca) #check out the components

Two plots: One plot of the PCA colored according to genus, with convex hulls surrounding the genera. It looks like this reflects a latitudinal gradient in temperature! You can interact with the PCA plot by clicking on points to view associated metadata. You can isolate the genus you want to view by double clicking the genus in the legend! You can also remove a genus by clicking on it once. There’s some other functionality you can explore in the toolbar at the top of the plot.

#add pca results to loc.clim data frame
loc.clim <- data.frame(loc.clim, clim.pca$x)

Error in data.frame(loc.clim, clim.pca$x) : 
  arguments imply differing number of rows: 568, 19

#plot tables
summary.pca

Importance of components:
                          PC1    PC2     PC3     PC4     PC5     PC6     PC7     PC8     PC9
Standard deviation     2.8205 2.5959 1.29925 1.03634 0.86397 0.75029 0.35359 0.22905 0.13868
Proportion of Variance 0.4187 0.3547 0.08885 0.05653 0.03929 0.02963 0.00658 0.00276 0.00101
Cumulative Proportion  0.4187 0.7734 0.86222 0.91874 0.95803 0.98766 0.99424 0.99700 0.99801
                          PC10    PC11   PC12    PC13    PC14    PC15    PC16    PC17    PC18
Standard deviation     0.11203 0.09749 0.0756 0.07171 0.04711 0.03566 0.03063 0.01582 0.01221
Proportion of Variance 0.00066 0.00050 0.0003 0.00027 0.00012 0.00007 0.00005 0.00001 0.00001
Cumulative Proportion  0.99867 0.99917 0.9995 0.99975 0.99986 0.99993 0.99998 0.99999 1.00000
                            PC19
Standard deviation     7.859e-16
Proportion of Variance 0.000e+00
Cumulative Proportion  1.000e+00

knitr::kable(round(clim.pca$rotation[,1:3],3)) #Table of loading scores for the first 3 PCs. 

	PC1	PC2	PC3
bio1_411	-0.343	-0.023	-0.148
bio2_411	0.248	0.051	-0.528
bio3_411	-0.133	0.040	-0.425
bio4_411	0.302	0.062	-0.295
bio5_411	-0.297	-0.009	-0.376
bio6_411	-0.352	-0.029	0.000
bio7_411	0.284	0.041	-0.420
bio8_411	-0.191	0.046	-0.205
bio9_411	-0.297	-0.060	0.060
bio10_411	-0.332	-0.017	-0.220
bio11_411	-0.349	-0.034	-0.072
bio12_411	0.048	-0.381	-0.005
bio13_411	0.009	-0.381	-0.033
bio14_411	0.050	-0.372	-0.064
bio15_411	-0.208	-0.006	-0.057
bio16_411	0.004	-0.382	-0.016
bio17_411	0.076	-0.372	-0.024
bio18_411	0.081	-0.364	-0.073
bio19_411	-0.038	-0.369	0.002

PCA-Species

These are PCAs of environmental space for species within genera. Each climate PCA is of localities for a single genus, colored by species. I’m doing this even for genera with one species, so it’s easy to see if certain localities group together.

Acanthoxyla

#source function to conduct a PCA on individual species
summary.list.acan <- species_pca_fun(loc.clim, "acanthoxyla")
#plot
plot_clim_pca(summary.list.acan$loc.clim, summary.list.acan$summary.pca)

Ignoring unknown aesthetics: text

summary.list.acan$summary.pca

Importance of components:
                          PC1    PC2    PC3     PC4     PC5     PC6     PC7     PC8     PC9
Standard deviation     2.8976 2.4081 1.4499 1.03416 0.99391 0.64837 0.37316 0.17888 0.15065
Proportion of Variance 0.4419 0.3052 0.1106 0.05629 0.05199 0.02213 0.00733 0.00168 0.00119
Cumulative Proportion  0.4419 0.7471 0.8578 0.91404 0.96603 0.98816 0.99549 0.99717 0.99836
                          PC10    PC11    PC12    PC13    PC14    PC15    PC16    PC17
Standard deviation     0.10865 0.07958 0.07073 0.05713 0.05208 0.03016 0.02200 0.01953
Proportion of Variance 0.00062 0.00033 0.00026 0.00017 0.00014 0.00005 0.00003 0.00002
Cumulative Proportion  0.99899 0.99932 0.99958 0.99975 0.99990 0.99994 0.99997 0.99999
                          PC18      PC19
Standard deviation     0.01351 4.091e-16
Proportion of Variance 0.00001 0.000e+00
Cumulative Proportion  1.00000 1.000e+00

loadings.acan <- summary.list.acan$summary.pca$rotation
knitr::kable(round(loadings.acan[,1:3],3)) #Table of loading scores for the first 3 PCs. 

	PC1	PC2	PC3
bio1_411	-0.220	-0.303	0.131
bio2_411	0.191	0.155	0.499
bio3_411	-0.062	0.141	0.324
bio4_411	0.244	0.106	0.354
bio5_411	-0.152	-0.279	0.381
bio6_411	-0.256	-0.274	-0.004
bio7_411	0.232	0.117	0.434
bio8_411	-0.027	-0.275	-0.091
bio9_411	-0.251	-0.172	0.116
bio10_411	-0.197	-0.308	0.204
bio11_411	-0.243	-0.289	0.059
bio12_411	0.284	-0.232	-0.046
bio13_411	0.268	-0.253	0.009
bio14_411	0.289	-0.219	-0.049
bio15_411	-0.146	-0.087	0.300
bio16_411	0.264	-0.256	-0.004
bio17_411	0.293	-0.211	-0.065
bio18_411	0.295	-0.205	-0.054
bio19_411	0.220	-0.277	0.039

Argosarchus

#conduct pca
summary.list.argo <- species_pca_fun(loc.clim, "argosarchus")
#plot
plot_clim_pca(summary.list.argo$loc.clim, summary.list.argo$summary.pca)

Ignoring unknown aesthetics: text

summary.list.argo$summary.pca

Importance of components:
                          PC1    PC2    PC3     PC4     PC5     PC6    PC7    PC8    PC9
Standard deviation     2.6107 2.5769 1.5880 1.08155 0.94245 0.84133 0.3698 0.2092 0.1509
Proportion of Variance 0.3587 0.3495 0.1327 0.06157 0.04675 0.03725 0.0072 0.0023 0.0012
Cumulative Proportion  0.3587 0.7082 0.8409 0.90251 0.94926 0.98652 0.9937 0.9960 0.9972
                          PC10    PC11    PC12    PC13    PC14    PC15    PC16    PC17
Standard deviation     0.13650 0.12389 0.08684 0.07717 0.05097 0.03317 0.02797 0.02345
Proportion of Variance 0.00098 0.00081 0.00040 0.00031 0.00014 0.00006 0.00004 0.00003
Cumulative Proportion  0.99820 0.99900 0.99940 0.99971 0.99985 0.99991 0.99995 0.99998
                          PC18      PC19
Standard deviation     0.02016 3.848e-16
Proportion of Variance 0.00002 0.000e+00
Cumulative Proportion  1.00000 1.000e+00

loadings.argo <- summary.list.argo$summary.pca$rotation
knitr::kable(round(loadings.argo[,1:3],3)) #Table of loading scores for the first 3 PCs. 

	PC1	PC2	PC3
bio1_411	0.253	-0.268	-0.137
bio2_411	-0.139	0.198	-0.487
bio3_411	0.018	0.020	-0.421
bio4_411	-0.210	0.213	-0.300
bio5_411	0.192	-0.174	-0.437
bio6_411	0.254	-0.286	0.040
bio7_411	-0.166	0.222	-0.418
bio8_411	-0.038	-0.077	0.082
bio9_411	0.223	-0.227	-0.115
bio10_411	0.239	-0.247	-0.233
bio11_411	0.265	-0.272	-0.049
bio12_411	0.281	0.261	0.038
bio13_411	0.303	0.232	-0.003
bio14_411	0.246	0.289	0.045
bio15_411	0.133	-0.160	-0.152
bio16_411	0.307	0.228	0.007
bio17_411	0.248	0.289	0.046
bio18_411	0.225	0.305	0.047
bio19_411	0.331	0.173	-0.032

Asteliaphasma

#pca
summary.list.aste <- species_pca_fun(loc.clim, "asteliaphasma")
#plot
plot_clim_pca(summary.list.aste$loc.clim, summary.list.aste$summary.pca)

Ignoring unknown aesthetics: text

summary.list.aste$summary.pca

Importance of components:
                          PC1    PC2     PC3     PC4     PC5     PC6     PC7     PC8     PC9
Standard deviation     3.5289 1.9449 1.08847 0.93035 0.68419 0.40024 0.19212 0.13894 0.10016
Proportion of Variance 0.6554 0.1991 0.06236 0.04556 0.02464 0.00843 0.00194 0.00102 0.00053
Cumulative Proportion  0.6554 0.8545 0.91687 0.96242 0.98706 0.99549 0.99743 0.99845 0.99898
                          PC10    PC11    PC12    PC13    PC14    PC15    PC16    PC17
Standard deviation     0.09172 0.05687 0.05344 0.04780 0.03677 0.02653 0.02020 0.01274
Proportion of Variance 0.00044 0.00017 0.00015 0.00012 0.00007 0.00004 0.00002 0.00001
Cumulative Proportion  0.99942 0.99959 0.99974 0.99986 0.99993 0.99997 0.99999 1.00000
                            PC18      PC19
Standard deviation     9.137e-16 2.186e-16
Proportion of Variance 0.000e+00 0.000e+00
Cumulative Proportion  1.000e+00 1.000e+00

loadings.aste <- summary.list.aste$summary.pca$rotation
knitr::kable(round(loadings.aste[,1:3],3)) #Table of loading scores for the first 3 PCs. 

	PC1	PC2	PC3
bio1_411	-0.264	-0.159	-0.068
bio2_411	0.226	0.164	-0.445
bio3_411	-0.069	-0.207	-0.688
bio4_411	0.243	0.193	-0.241
bio5_411	-0.245	-0.123	-0.322
bio6_411	-0.261	-0.190	0.087
bio7_411	0.234	0.203	-0.314
bio8_411	-0.264	-0.175	0.009
bio9_411	-0.225	-0.102	-0.134
bio10_411	-0.260	-0.151	-0.114
bio11_411	-0.264	-0.177	-0.001
bio12_411	0.239	-0.272	0.017
bio13_411	0.203	-0.349	-0.021
bio14_411	0.230	-0.260	0.112
bio15_411	-0.148	-0.237	-0.093
bio16_411	0.210	-0.341	0.022
bio17_411	0.246	-0.227	0.041
bio18_411	0.229	-0.275	-0.022
bio19_411	0.210	-0.341	0.021

Marginal climate hypothesis workspace. Resample from sister species data set and calculate average per sample. Compare absolute value of range-restricted species to distribution of sister species averages. Need to work on a suitable statistical test.

#calculate the centroid of a random sample of individuals. df = data frame, sp = string containing the species you are interested (e.g. "naomi"), len = the number of individuals to sample. Should be the number of individuals from the species that has fewer occurrences.
#calculate the centroid from the range-restricted species. 
pc.centroid.nov <- summary.list.aste$loc.clim %>% 
  filter(species == "nov. sp.") %>%
  select(PC1.1:PC3.1) %>%
  summarize_all(mean) %>% 
  rowMeans() %>%
  abs()
#resample the more widespread species many times, calculating the centroid of three individuals (number of individuals in the range-restricted species)
pc.centroid.naomi <- replicate(1000, pc_centroid_fun(summary.list.aste$loc.clim, "naomi", 3), simplify = TRUE) %>% 
  as.data.frame()
names(pc.centroid.naomi) <- "centroid" #needs to be a data frame with a named column for ggplot
#sampling distribution of the centroids calculated from the generalist species. The red line indicates the centroid of the range-restricted species
ggplot(pc.centroid.naomi, aes(x = centroid)) +
  geom_histogram(bins = 30) +
  #scale_x_sqrt() +
  geom_vline(xintercept = pc.centroid.nov, color = "red") + 
  theme_linedraw()

Outlying Mean Index. Another test of the marginal niche hypothesis.

aste_omi$test_omi

class: krandtest lightkrandtest 
Monte-Carlo tests
Call: as.krandtest(sim = t(sim), obs = obs)

Number of tests:   3 

Adjustment method for multiple comparisons:   none 
Permutation number:   1000 

NA

Clitarchus

summary.list.clita <- species_pca_fun(loc.clim, "clitarchus")
plot_clim_pca(summary.list.clita$loc.clim, summary.list.clita$summary.pca)

Ignoring unknown aesthetics: text

summary.list.clita$summary.pca

Importance of components:
                          PC1    PC2     PC3    PC4     PC5     PC6    PC7     PC8     PC9
Standard deviation     2.8287 2.6276 1.32815 1.1156 0.73394 0.53892 0.3776 0.22177 0.14594
Proportion of Variance 0.4211 0.3634 0.09284 0.0655 0.02835 0.01529 0.0075 0.00259 0.00112
Cumulative Proportion  0.4211 0.7845 0.87737 0.9429 0.97121 0.98650 0.9940 0.99659 0.99771
                          PC10    PC11    PC12    PC13    PC14    PC15    PC16    PC17
Standard deviation     0.13870 0.10155 0.07717 0.06308 0.04870 0.02999 0.01809 0.01515
Proportion of Variance 0.00101 0.00054 0.00031 0.00021 0.00012 0.00005 0.00002 0.00001
Cumulative Proportion  0.99873 0.99927 0.99958 0.99979 0.99992 0.99996 0.99998 0.99999
                          PC18      PC19
Standard deviation     0.01187 5.086e-16
Proportion of Variance 0.00001 0.000e+00
Cumulative Proportion  1.00000 1.000e+00

loadings.clita <- summary.list.clita$summary.pca$rotation
knitr::kable(round(loadings.clita[,1:3],3)) #Table of loading scores for the first 3 PCs. 

	PC1	PC2	PC3
bio1_411	-0.317	-0.142	-0.099
bio2_411	0.129	0.256	-0.457
bio3_411	-0.166	0.081	-0.530
bio4_411	0.252	0.216	-0.236
bio5_411	-0.305	-0.055	-0.299
bio6_411	-0.304	-0.191	0.037
bio7_411	0.182	0.251	-0.355
bio8_411	-0.189	-0.209	0.105
bio9_411	-0.280	-0.066	-0.167
bio10_411	-0.314	-0.119	-0.152
bio11_411	-0.318	-0.157	-0.040
bio12_411	-0.176	0.322	0.126
bio13_411	-0.207	0.294	0.060
bio14_411	-0.180	0.303	0.161
bio15_411	-0.140	-0.061	-0.250
bio16_411	-0.211	0.293	0.078
bio17_411	-0.145	0.332	0.151
bio18_411	-0.149	0.325	0.149
bio19_411	-0.216	0.289	0.067

Marginal environment hypothesis

#calculate the centroid from the range-restricted species. 
pc.centroid.tepaki <- summary.list.clita$loc.clim %>% 
  filter(species == "tepaki") %>%
  select(PC1.1:PC3.1) %>%
  summarize_all(mean) %>% 
  rowMeans() %>%
  abs()
pc.centroid.hookeri <- replicate(1000, pc_centroid_fun(summary.list.clita$loc.clim, "hookeri", 3), simplify = TRUE) %>% 
  as.data.frame()
names(pc.centroid.hookeri) <- "centroid"
ggplot(pc.centroid.hookeri, aes(x = centroid)) +
  geom_histogram(bins = 30) +
  #scale_x_sqrt() +
  geom_vline(xintercept = pc.centroid.tepaki, color = "red") + 
  theme_linedraw()

#length(pc.centroid.hookeri$centroid[pc.centroid.hookeri$centroid > pc.centroid.tepaki])

Outlying Mean Index. Another test of the marginal niche hypothesis.

clita_omi$test_omi

class: krandtest lightkrandtest 
Monte-Carlo tests
Call: as.krandtest(sim = t(sim), obs = obs)

Number of tests:   3 

Adjustment method for multiple comparisons:   none 
Permutation number:   1000 

NA

Micrarchus

summary.list.micra <- species_pca_fun(loc.clim, "micrarchus")
plot_clim_pca(summary.list.micra$loc.clim, summary.list.micra$summary.pca)

Ignoring unknown aesthetics: text

summary.list.micra$summary.pca

Importance of components:
                          PC1    PC2    PC3     PC4     PC5     PC6     PC7     PC8     PC9
Standard deviation     3.4602 1.8070 1.4755 1.04628 0.47265 0.37427 0.28044 0.13523 0.12413
Proportion of Variance 0.6302 0.1719 0.1146 0.05762 0.01176 0.00737 0.00414 0.00096 0.00081
Cumulative Proportion  0.6302 0.8020 0.9166 0.97422 0.98598 0.99335 0.99749 0.99846 0.99927
                          PC10    PC11    PC12    PC13    PC14    PC15    PC16    PC17
Standard deviation     0.08040 0.04868 0.04396 0.03954 0.02696 0.01967 0.01488 0.01171
Proportion of Variance 0.00034 0.00012 0.00010 0.00008 0.00004 0.00002 0.00001 0.00001
Cumulative Proportion  0.99961 0.99973 0.99983 0.99992 0.99995 0.99998 0.99999 0.99999
                          PC18      PC19
Standard deviation     0.01059 2.802e-16
Proportion of Variance 0.00001 0.000e+00
Cumulative Proportion  1.00000 1.000e+00

loadings.micra <- summary.list.micra$summary.pca$rotation
knitr::kable(round(loadings.micra[,1:3],3)) #Table of loading scores for the first 3 PCs. 

	PC1	PC2	PC3
bio1_411	0.265	0.140	0.187
bio2_411	0.044	-0.384	0.474
bio3_411	0.215	-0.052	0.376
bio4_411	-0.145	-0.454	0.113
bio5_411	0.264	0.036	0.260
bio6_411	0.264	0.203	0.092
bio7_411	-0.069	-0.439	0.365
bio8_411	0.183	0.271	0.080
bio9_411	0.265	0.137	0.127
bio10_411	0.266	0.105	0.207
bio11_411	0.264	0.171	0.164
bio12_411	-0.259	0.189	0.187
bio13_411	-0.253	0.205	0.199
bio14_411	-0.256	0.177	0.201
bio15_411	0.130	0.077	0.062
bio16_411	-0.252	0.206	0.204
bio17_411	-0.256	0.184	0.209
bio18_411	-0.255	0.186	0.211
bio19_411	-0.254	0.175	0.189

Niveaphasma

summary.list.nive <- species_pca_fun(loc.clim, "niveaphasma")
plot_clim_pca(summary.list.nive$loc.clim, summary.list.nive$summary.pca)

Ignoring unknown aesthetics: text

summary.list.nive$summary.pca

Importance of components:
                          PC1    PC2    PC3     PC4     PC5     PC6     PC7     PC8     PC9
Standard deviation     2.9075 2.3439 1.6667 1.03074 0.77498 0.58305 0.48456 0.11336 0.09999
Proportion of Variance 0.4449 0.2892 0.1462 0.05592 0.03161 0.01789 0.01236 0.00068 0.00053
Cumulative Proportion  0.4449 0.7341 0.8803 0.93621 0.96782 0.98571 0.99807 0.99874 0.99927
                          PC10    PC11    PC12    PC13    PC14    PC15    PC16    PC17
Standard deviation     0.07972 0.05147 0.04226 0.03754 0.02765 0.02184 0.01340 0.01209
Proportion of Variance 0.00033 0.00014 0.00009 0.00007 0.00004 0.00003 0.00001 0.00001
Cumulative Proportion  0.99960 0.99974 0.99984 0.99991 0.99995 0.99998 0.99999 0.99999
                          PC18      PC19
Standard deviation     0.01062 7.143e-16
Proportion of Variance 0.00001 0.000e+00
Cumulative Proportion  1.00000 1.000e+00

loadings.nive <- summary.list.nive$summary.pca$rotation
knitr::kable(round(loadings.nive[,1:3],3)) #Table of loading scores for the first 3 PCs. 

	PC1	PC2	PC3
bio1_411	-0.212	-0.286	0.234
bio2_411	-0.053	0.355	0.221
bio3_411	-0.050	-0.292	-0.117
bio4_411	-0.042	0.388	0.209
bio5_411	-0.218	0.082	0.424
bio6_411	-0.139	-0.385	0.066
bio7_411	-0.027	0.387	0.230
bio8_411	-0.218	-0.008	0.258
bio9_411	-0.002	-0.238	0.191
bio10_411	-0.245	-0.148	0.347
bio11_411	-0.155	-0.369	0.118
bio12_411	0.322	-0.071	0.184
bio13_411	0.314	-0.077	0.217
bio14_411	0.329	-0.061	0.130
bio15_411	-0.150	0.011	0.384
bio16_411	0.315	-0.087	0.205
bio17_411	0.330	-0.054	0.145
bio18_411	0.319	-0.067	0.185
bio19_411	0.326	-0.079	0.148

Spinotectarchus

summary.list.spin <- species_pca_fun(loc.clim, "spinotectarchus")
plot_clim_pca(summary.list.spin$loc.clim, summary.list.spin$summary.pca)

Ignoring unknown aesthetics: text

summary.list.spin$summary.pca

Importance of components:
                          PC1    PC2     PC3     PC4     PC5     PC6     PC7     PC8     PC9
Standard deviation     3.6740 1.7717 1.04961 0.74836 0.67601 0.41693 0.17179 0.13411 0.09313
Proportion of Variance 0.7105 0.1652 0.05798 0.02948 0.02405 0.00915 0.00155 0.00095 0.00046
Cumulative Proportion  0.7105 0.8757 0.93363 0.96311 0.98716 0.99631 0.99786 0.99881 0.99927
                          PC10    PC11    PC12    PC13    PC14    PC15    PC16      PC17
Standard deviation     0.07134 0.05938 0.05019 0.03604 0.02482 0.02193 0.01971 6.967e-16
Proportion of Variance 0.00027 0.00019 0.00013 0.00007 0.00003 0.00003 0.00002 0.000e+00
Cumulative Proportion  0.99954 0.99972 0.99985 0.99992 0.99995 0.99998 1.00000 1.000e+00
                          PC18      PC19
Standard deviation     1.6e-17 2.958e-18
Proportion of Variance 0.0e+00 0.000e+00
Cumulative Proportion  1.0e+00 1.000e+00

loadings.spin <- summary.list.spin$summary.pca$rotation
knitr::kable(round(loadings.spin[,1:3],3)) #Table of loading scores for the first 3 PCs. 

	PC1	PC2	PC3
bio1_411	-0.257	-0.130	-0.194
bio2_411	0.230	0.165	-0.351
bio3_411	-0.106	-0.360	-0.197
bio4_411	0.230	0.233	-0.239
bio5_411	-0.239	-0.097	-0.390
bio6_411	-0.254	-0.197	0.014
bio7_411	0.228	0.235	-0.273
bio8_411	-0.258	-0.165	-0.104
bio9_411	-0.215	-0.014	-0.395
bio10_411	-0.252	-0.109	-0.265
bio11_411	-0.258	-0.165	-0.104
bio12_411	0.239	-0.264	-0.037
bio13_411	0.220	-0.323	0.010
bio14_411	0.240	-0.237	-0.137
bio15_411	-0.152	-0.249	0.447
bio16_411	0.221	-0.322	0.029
bio17_411	0.247	-0.211	-0.129
bio18_411	0.238	-0.241	-0.172
bio19_411	0.221	-0.322	0.029

Marginal environment hypothesis

#calculate the centroid from the range-restricted species. 
pc.centroid.acornutus_sub <- summary.list.spin$loc.clim %>% 
  filter(species == "acornutus_sub") %>%
  select(PC1.1:PC3.1) %>%
  summarize_all(mean) %>% 
  rowMeans() %>%
  abs()
pc.centroid.acornutus <- replicate(1000, pc_centroid_fun(summary.list.spin$loc.clim, "acornutus", 3), simplify = TRUE) %>% 
  as.data.frame()
names(pc.centroid.acornutus) <- "centroid"
ggplot(pc.centroid.acornutus, aes(x = centroid)) +
  geom_histogram(bins = 30) +
  #scale_x_sqrt() +
  geom_vline(xintercept = pc.centroid.acornutus_sub, color = "red") + 
  theme_linedraw()

Outlying Mean Index. Another test of the marginal niche hypothesis.

spin_omi$test_omi

class: krandtest lightkrandtest 
Monte-Carlo tests
Call: as.krandtest(sim = t(sim), obs = obs)

Number of tests:   3 

Adjustment method for multiple comparisons:   none 
Permutation number:   1000 

NA

Tectarchus

summary.list.tect <- species_pca_fun(loc.clim, "tectarchus")
plot_clim_pca(summary.list.tect$loc.clim, summary.list.tect$summary.pca)

Ignoring unknown aesthetics: text

summary.list.tect$summary.pca

Importance of components:
                          PC1    PC2    PC3     PC4     PC5     PC6     PC7    PC8     PC9
Standard deviation     2.7649 2.5672 1.5947 1.13698 0.63754 0.57252 0.35428 0.1689 0.11908
Proportion of Variance 0.4024 0.3469 0.1338 0.06804 0.02139 0.01725 0.00661 0.0015 0.00075
Cumulative Proportion  0.4024 0.7492 0.8831 0.95112 0.97251 0.98976 0.99637 0.9979 0.99862
                          PC10    PC11    PC12    PC13    PC14    PC15    PC16    PC17
Standard deviation     0.11043 0.07835 0.05082 0.04736 0.04012 0.02414 0.02156 0.01715
Proportion of Variance 0.00064 0.00032 0.00014 0.00012 0.00008 0.00003 0.00002 0.00002
Cumulative Proportion  0.99926 0.99958 0.99972 0.99984 0.99992 0.99995 0.99998 0.99999
                          PC18      PC19
Standard deviation     0.01214 4.565e-16
Proportion of Variance 0.00001 0.000e+00
Cumulative Proportion  1.00000 1.000e+00

loadings.tect <- summary.list.tect$summary.pca$rotation
knitr::kable(round(loadings.tect[,1:3],3)) #Table of loading scores for the first 3 PCs. 

	PC1	PC2	PC3
bio1_411	0.309	-0.182	0.117
bio2_411	-0.122	0.137	0.539
bio3_411	0.159	-0.033	0.464
bio4_411	-0.214	0.247	0.289
bio5_411	0.273	-0.146	0.318
bio6_411	0.306	-0.201	-0.020
bio7_411	-0.175	0.158	0.465
bio8_411	0.221	-0.137	-0.105
bio9_411	0.268	-0.200	0.100
bio10_411	0.305	-0.167	0.181
bio11_411	0.304	-0.205	0.060
bio12_411	-0.211	-0.315	0.021
bio13_411	-0.209	-0.310	0.040
bio14_411	-0.214	-0.304	0.069
bio15_411	0.058	0.027	0.082
bio16_411	-0.204	-0.316	0.036
bio17_411	-0.216	-0.306	0.038
bio18_411	-0.223	-0.299	0.038
bio19_411	-0.197	-0.314	0.061

Tepakiphasma

Nothing. Only one locality.

OMI_all

Outlying Mean Index. Another test of the marginal niche hypothesis.

all_omi$test_omi

class: krandtest lightkrandtest 
Monte-Carlo tests
Call: as.krandtest(sim = t(sim), obs = obs)

Number of tests:   17 

Adjustment method for multiple comparisons:   none 
Permutation number:   1000 

NA